Involutive quantales and quantale-enriched involutive topological spaces
Operator Algebras
2025-09-11 v2 General Topology
Abstract
In this paper, we provide a comprehensive analysis of involutive quantales, with a particular focus on quantic frames. We extend the axiomatic foundations of quantale-enriched topological spaces to include closure under the anti-homomorphic involution, facilitating a balanced topologization of the spectrum of unital -algebras that encompasses both closed right and left ideals through the concept of quantic frames. Specifically, certain subspaces of pure states are identified as strongly Hausdorff separated quantale-enriched involutive topological spaces.
Keywords
Cite
@article{arxiv.2503.03498,
title = {Involutive quantales and quantale-enriched involutive topological spaces},
author = {Javier Gutiérrez García and Ulrich Höhle},
journal= {arXiv preprint arXiv:2503.03498},
year = {2025}
}